In traditional RF communications, a message in analog or digital data, audio, or video communications is impressed in various ways on a RF sinusoidal carrier at the transmitter, and a faithful reproduction of the original message is recovered from this modulated signal at the receiver. This transmitter modulation and receiver demodulation process relies on the classical synchronization or entrainment of periodic signals that has been well established for decades, resulting in a myriad of strategies to enhance the synchronization process and to overcome the many impairments to the modulated signal that can take place in a communication channel between the transmitter and receiver. Currently these systems are dominated by digital implementations, wherein the original analog message is sampled, quantized, encrypted, and error-correction encoded to provide the resulting digital data stream. The data in the data stream is then grouped into a finite number of symbol states that are modulated onto an RF carrier in a manner suitable for demodulation upon reception. While suitable in many communication applications, there still are several applications where digital technology does not sufficiently meet performance demands, thereby still requiring the use of analog communications.
With the advent of chaotic synchronization, researchers have begun to explore the replacement of the sinusoidal carrier with a generalized chaotic carrier in order to exploit the special properties of chaos and chaotic synchronization. In addition to the many means discovered to achieve chaotic synchronization, there have also been an equally large set of techniques developed to combine the chaos with the message in a recoverable manner. Two of the four basic forms of chaotic synchronization are considered to illustrate chaotic synchronization techniques applicable to communications. In one form, an original and most often used master-slave form is usually based on unforced chaotic oscillators, whereas the second form is a non-autonomous form that employs forced chaotic oscillators. In the simplest case of the master-slave approach, an autonomous unforced or self-oscillating chaotic system is divided into two subsystems, one of which is replicated remotely and called the response subsystem, while the other is a drive subsystem used to unidirectionally drive the response subsystem through a communication channel, as do traditional transmitters and receivers. The replicated response subsystem and drive subsystems must be of identical topology with precise parameter matching for synchronization. Such chaotic communication systems provide for the enhanced security of the communication channel due to the inherent noise resemblance of the chaotic carrier signal. The remaining driving subsystem is usually chosen to be one dimensional in view of channel bandwidth efficiency considerations. These chaotic systems may include rigorous conditions for lock and system decomposition methods.
A more recent approach involves the use of identical non-autonomous, forced chaotic systems. In the forced chaotic communication systems, the drive and response systems are unidirectionally linked, again preferably through only one state variable, and the frequency .omega..sup.R and phase .phi..sup.R of the receiver forcing function is adaptively adjusted to achieve lock through the use of an error signal, derived from an x driving signal and the locally generated x' response signal. This forced chaotic system generalizes the classical phase locked loop for sinusoidal signals. Such an arrangement has been shown to be significantly robust to channel interference favorable for real world applications.
The motivation for applying chaos to communications lies in the basic aspects associated with the carrier, namely, the generation, synchronization, modulation and demodulation with information. The basic characteristics of chaos, specifically its noise resemblance spectral appearance generated from a well defined and often simple underlying dynamical rule, renders chaotic signals a natural candidate for hiding information with the dynamical rule as the key, implying both low probability of intercept and encryption capabilities. The synchronization process itself may prove superior to classical acquisition schemes with respect to speed, robustness, immunity to channel impairments and filtering, and implementation complexity. Furthermore, chaotic modulation may provide many new capabilities not even possible with traditional approaches, such as unique privacy and frequency re-use features for analog communications, tolerance to amplifier nonlinearities, and indirect schemes that have enhanced security and multiplexing characteristics.
The first and most fundamental task in developing chaos-based communications is the hardware design and implementation of the chaotic carrier generator. These chaotic generators must be readily designed, fabricated, and matched, and have the reliability of traditional sinusoidal carrier generators in order to compete with current communication systems. At this early stage in the technology development, the design of chaotic dynamical systems, let alone realizable hardware implementations, is essentially an art with very few systematic guidelines. One historical factor that has caused this situation is that chaos has become a desired behavior in engineering systems only recently marked by the announcement of chaotic synchronization. In the same way, it is only recently that powerful simulation tools have become readily available to allow the numerical experiments needed to investigate chaotic systems.
Several chaos implementations have emerged, divided between those that operate at baseband frequencies and those that run at the higher radio frequency (RF) and microwave regime. Either of these generator classes can be applied to RF communications, with the first requiring traditional frequency upconversion and downconversion. The first class consists of autonomous analog oscillator circuits, such as the canonical piecewise-linear (PWL) Chua circuit, consists of nonautonomous analog oscillator circuits, such as the forced Chua circuit, and consists of mapping-based digital circuits. The autonomous canonical PWL Chua circuit oscillator was among the first investigated to serve as the basis for a high-frequency chaos-based communications link. The oscillator circuit includes a realization of a single nonlinear resistor providing a representative PWL I-V characteristic that is locally active and globally passive.
The well-known Duffing equation is one of several prototypical nonautonomous systems that can exhibit chaotic behavior and emerged in the study of mechanical systems typically that operate in the low frequency regime. The mechanical systems described by the Duffing equation and that can produce chaotic behavior do not use feedback. As a consequence, these systems do not address problems relating to the use of feedback, such as phase delay in the feedback path.
The second class of implementations consists of suitably driven analog phase-locked loops that can place, through a frequency modulation process, a desired bandwidth of chaos around a chosen RF carrier frequency, and contains a baseband oscillator based on the use of active circuits that produce negative resistance, such as those containing diodes and transistor amplifiers.
It is desirable to handle wideband data streams that are common in military and commercial systems, such as high-resolution imagery and broadcast quality video, respectively. The bandwidth of the chaotic carrier must necessarily be larger than that of the message. Wideband chaotic oscillators can be an alternative to the second class of oscillators that can have some limitations in wideband data stream communication applications. These wideband oscillators could provide carriers for RF communications, or provide a subcarrier placed upon a traditional sinusoidal carrier at some desired center frequency.
Several modulation methods have been proposed that reversibly combine information with the signal produced by a chaotic generator. These methods include additive masking, angle modulation, multiplicative mixing, chaos shift keying, generalized modulation, and indirect parameter modulation, as well as forming chaotic signal constellations by applying control chaos techniques to the generator. It is clear that whatever method is used, the channel bandwidth will be limited by the bandwidth of the generator. For this reason, and in order to provide communications capabilities for wideband information payloads, such as high-resolution imagery and video, it is extremely desirable to extend the generator bandwidth as much as possible. Prior systems have not effectively exploited the increased bandwidth available from an enhanced chaotic carrier generator.
To date, most of the methods used to generate chaotic oscillations fall into four main categories, mapping-based digital circuits, forced or unforced baseband analog circuits, microwave analog circuits based on active tunnel-effect devices, and suitably driven analog phase-locked loops (PLLs). The output spectrum of the digital circuits is limited to a fraction of the clock rate of the digital circuitry used to implement the map. Baseband analog circuits have relied on the production of negative resistance, an impedance with a large negative real part, using operational amplifiers or discrete transistors. This impedance will not be frequency independent at higher operating frequencies due to propagation delay and other parasitics within the amplifiers used in production of the high operating frequencies. This propagation delay severely limits the bandwidth of the resulting chaotic generator. Tunnel-effect devices are capable of operation at microwave frequencies, but contain inherent nonlinearities that are difficult to control because the I-V and Z-V characteristics are semiconductor process dependent. These inherent nonlinearities translate into difficulty in synchronizing two supposedly identical generators. The PLL approach is a means to frequency modulate a voltage controlled oscillator (VCO) with a baseband chaotic signal. The modulation index determines the extent to which the baseband signal is spread over the output spectrum. This PLL approach can be enhanced as the bandwidth of the modulating signal is increased.
There exist other techniques of generating chaos, including using echoes in an electrically long unterminated transmission line placed in a feedback path around a nonlinear amplifier, and repeated frequency multiplication of a baseband chaotic signal, for which synchronization has not been demonstrated, and is likely to be difficult to achieve. In particular, for the nonlinear amplifier with echoing transmission line feedback, an infinite dimensional system results with behavior that is quite sensitive to the value of the delay, a negative attribute for synchronization purposes. The sequential frequency multiplication approach has an ill-defined dynamical system and an implementation that will make it difficult to systematically synchronize. These and other disadvantages are solved or reduced using the invention.